Mathematical Communication of Vocational Students with Field Dependent and Independent Cognitive Styles in Solving Linear Programming Problems

Dasa Ismaimuza, Rita Lefrida, Silvana, Baiduri

Abstract

This study aimed to investigate and compare the mathematical communication skills of vocational students with field-independent and field-dependent cognitive styles when solving linear programming problems. The goal was to investigate how these cognitive styles affect the effectiveness of mathematical communication, which includes understanding, planning, and expressing solutions. Data were obtained qualitatively from two vocational students: one with a field-independent cognitive style and the other with a field-dependent cognitive style. The data were analyzed using interactive analysis, which included codification, presentation, and conclusion. The findings revealed that students with a field-independent cognitive style had better mathematical communication skills than their field-dependent counterparts, particularly in understanding and planning solutions to linear programming problems. This study also discovered that both cognitive styles can effectively use different forms of mathematical communication, such as mathematical expressions, depictions, and text writing, particularly when answering questions. This study is unique in that it focuses on the role of cognitive styles in mathematical communication within the context of vocational education, thus providing insights into how educators can design more inclusive mathematics learning experiences that cater to different cognitive styles.

 

Keywords: mathematical communication; vocational students; field independent; field dependent; problem solving; linear programming

 

https://doi.org/10.55463/issn.1674-2974.51.8.1

 


Full Text:

PDF


References


OZDEMIR H. Maths instruction in vocational high school from teachers and students’ eyes: a different kettle of fish. Journal of Research in Mathematics Education, 2020, 9(2): 196, https://doi.org/10.17583/redimat.2020.3796.

MUHRMAN K. How can students in vocational education be motivated to learn mathematics? Nordic Journal of Vocational Education and Training, 2022, 12(3): 47–70, https://doi.org/10.3384/njvet.2242-458x.2212347.

RANI G., KUMAR P., DEVI R., et al. Mathematics as a Part of The Real Life. International Journal of Advanced Research in Science, Communication and Technology, 2023, 3(5): 409–418, https://doi.org/10.48175/ijarsct-11665.

NIKMAH N., and NUGRAHENI L. Analysis of Students’ Mathematical Communication Skills in Eight Grade of Junior high school on Number Patterns. Journal of Education and Learning Mathematics Research, 2023, 4(1): 20–30, https://doi.org/10.37303/jelmar.v4i1.106.

NOOR H. J. & AGOESTANTO A. Systematic Literature Review: Mathematical Communication Ability through Quantum Learning Model Based on Self Efficacy. Journal of Mathematics Education, 2023, 8(1): 1–17, https://doi.org/10.31327/jme.v8i1.1906.

POURDAVOOD B. R., MCCARTHY K., and MCCAFFERTY T. The impact of mental computation on children’s mathematical communication, problem solving, reasoning, and algebraic thinking. Athens Journal of Education, 2020, 7(3): 241–254, https://doi.org/10.30958/aje.7-3-1.

SHIH S. C., CHANG C. C., KUO B. C., and HUANG Y. H. Mathematics intelligent tutoring system for learning multiplication and division of fractions based on diagnostic teaching. Education and Information Technologies, 2023, 28(7): 9189–9210, https://doi.org/10.1007/s10639-022-11553-z.

ZEČEVIĆ M., BUSCH F. P., DHAMI D. S., and KERSTING K. Finding Structure and Causality in Linear Programs. Proceedings of the ICLR 2022 workshop on Objects, Structure and Causality: 1–8. https://doi.org/10.48550/arXiv.2203.15274

KUNWAR R., and SAPKOTA H. P. Introduction to Linear Programming Problems with Some Real-Life Applications. European Journal of Mathematics and Statistics, 2022, 3(2): 21–27, https://doi.org/10.24018/ejmath.2022.3.2.108.

DIAZ QUEZADA V. Difficulties and performance in mathematics competences: Solving problems with derivatives. International Journal of Engineering Pedagogy, 2020, 10(4): 35–53, https://doi.org/10.3991/ijep.v10i4.12473.

LAITH W., AL-SALIH R., and HABEEB A. A Novel Approach for Solving Decision Making Problems with Stochastic Linear Fractional Models. Eastern-European Journal of Enterprise Technologies, 2021, 5(4–113): 73–78, https://doi.org/10.15587/1729-4061.2021.241916.

JAELANI A. K., HASBI M., and BAHARULLAH B. A Critical Thinking Profile of Mathematics Education Students in Solving Ill-Structured Problem based on Mathematical Ability. Jurnal Teori dan Aplikasi Matematika, 2023, 7(2): 545, https://doi.org/10.31764/jtam.v7i2.13378.

FIRDAUS A. M., and HERWANDI H. Students’ Mathematics Problem-Solving Ability with Kinesthetic Learning Style at Vocational School. Lentera Pendidikan: Jurnal Ilmu Tarbiyah dan Keguruan, 2023, 26(1): 153–170, https://doi.org/10.24252/lp.2023v26n1i11.

DALBY D., and NOYES A. Mathematics curriculum waves within vocational education. Oxford Review of Education, 2022, 48(2): 166–183, https://doi.org/10.1080/03054985.2021.1940913.

PLACKLÉ I., KÖNINGS K.D., JACQUET W., et al. Improving student achievement through professional cultures of teaching in Flanders. European Journal of Education, 2022, 57(2): 325–341, https://doi.org/10.1111/ejed.12504.

SYUKRI A., MARZAL J., and MUHAIMIN M. Constructivism-Based Mathematics Learning Multimedia to Improve Students’ Mathematical Communication Skills. Indonesian Journal of Science and Mathematics Education, 2020, 3(2): 117–132, https://doi.org/10.24042/ijsme.v3i2.6201.

ANGGRAINI L., WULANDARI S., and NURMALA N. Errors of Class VIII Junior High School Students in Solving Mathematical Communication Problems Based on the Newman Procedure. Journal of Education and Learning Mathematics Research, 2022, 3(2): 103–108, https://doi.org/10.37303/jelmar.v3i2.80.

FAY N., BABYS u., and GELLA N.G.M. Analysis of Students’ Mathematical Communication Skills in Terms of Self-Confidence. International Journal of Humanities Education and Social Sciences), 2022, 1(5): 688–695, https://doi.org/10.55227/ijhess.v1i5.142.

SETYOWATI S., CHOLILY Y. M., and AZMI R. D. Analysis of Mathematical Communication Capabilities in Completing Problems in Matrix Materials Based on Solo Taxonomy. Mathematics Education Journal, 2020, 4(2): 166–176, https://doi.org/10.22219/mej.v4i2.12832.

ASTUTI N. R., GUNARHADI, and MINTASIH The Effect of RME on Mathematics Learning Outcomes Viewed Mathematic Communication Skills. International Journal of Educational Research Review, 2020, 5(1): 43–53, https://doi.org/10.24331/ijere.650864.

SINAMBELA P., NAPITUPULU E. E., and AMRY Z. Analysis of Mathematic Multiple Representations Ability by Applying the Problem-Based Learning Model (PBL) at Tenth Grade Students of SMA N 1 Pegagan Hilir. Proceedings of the 6th Annual International Seminar on Transformative Education and Educational Leadership (AISTEEL 2021), 2022, 591(Aisteel): 403–409, https://doi.org/10.2991/assehr.k.211110.116.

JEHADUS E., TAMUR M., MURNI V., et al. The Influence of Open-Ended Approach with Group-To-Group Strategy on the Improvement of Mathematic Communication Skills for High School Students. Proceedings of the 1st International Conference on Education, Humanities, Health and Agriculture, ICEHHA 2021, 3-4 June 2021, Ruteng, Flores, Indonesia, https://doi.org/10.4108/eai.3-6-2021.2310737.

HO S., and KOZHEVNIKOV M. Cognitive style and creativity: The role of education in shaping cognitive style profiles and creativity of adolescents. British Journal of Educational Psychology, 2023, 93(4): 978–996, https://doi.org/10.1111/bjep.12615.

BONAVITA A., BELLAGAMBA M., VERDE P., et al. The Effect of Cognitive Style on Individual Differences in Prismatic Adaptation: A Pilot Study. Brain Sciences, 2023, 13(4): 641 https://doi.org/10.3390/brainsci13040641.

BARANOVA E., RUBTSOVA D., RUMYANTSEVA N. et al. Considering cognitive styles when teaching the language to representatives of different cultures. E3S Web of Conferences, 2021, 284: 1–6, https://doi.org/10.1051/e3sconf/202128409009.

HAO X. et al. Individual differences in brain structure and resting brain function underlie cognitive styles: Evidence from the embedded figures test. PLoS ONE, 2013, 8(12): 1–9, https://doi.org/10.1371/journal.pone.0078089.

WIBAWA K. A., PRATIWI N. K. I. W., and WENA I. M. Analysis of student error based on Newman’s procedure in solving hots types reviewing from cognitive style FI and FD. Prima: Jurnal Pendidikan Matematika, 2023, 7(1): 1, https://doi.org/10.31000/prima.v7i1.6761.

YANG T. C. and CHEN S. Y. Investigating students’ online learning behavior with a learning analytic approach: field dependence/independence vs. holism/serialism. Interactive Learning Environments, 2023, 31(2): 1041–1059, https://doi.org/10.1080/10494820.2020.1817759.

LINAWATI, PATHUDDIN P., MUBARIK M., et al. Misconception of Student: Difference Field Independent-Dependent Cognitive Style. Proceedings of the 2021 Tadulako’s International Conference on Social Sciences (TICoSS 2021), 674(TICoSS 2021): 2022, 59–63, https://doi.org/10.2991/assehr.k.220707.014.

USOLIN K., SON A. L., MAIFA T. S., and GARCÍA-GARCÍA J. Profile of Mathematics Communication Ability of Seventh-Grade Students in Solving Set Problems Based on Cognitive Style. RANGE: Jurnal Pendidikan Matematika, 2023, 4(2): 189–201, https://doi.org/10.32938/jpm.v4i2.3593.

AFIFAH, SORO S., and FARADILLAH A. Mathematic Reasoning Ability Based on Cognitive Style Field Dependent, Field Intermediate, and Field Independent. Jurnal Pendidikan MIPA, 2022, 23(2): 681–691.

NURDIN N. Cognitive Reasoning and Style: Do Differences of Cognitive Style Result Differences in Reasoning Ability? Edumaspul: Jurnal Pendidikan, 2022, 6(2): 2546–2550, https://doi.org/10.33487/edumaspul.v6i2.3301.

CHASANAH C., RIYADI, and USODO B. The effectiveness of learning models on written mathematical communication skills viewed from students’ cognitive styles. European Journal of Educational Research, 2020, 9(3): 979–994, https://doi.org/10.12973/EU-JER.9.3.979.

SEPTIYANA W., ZARISTA R. H., and HASANAH R. Analysis of Algebra Communication Skills and Creative Thinking Skill Levels: In Terms of Cognitive Style. Alpha Math: Journal of Mathematics Education, 2023, 9(1): 42, https://doi.org/10.30595/alphamath.v9i1.15950.

POLO-BLANCO I., SUÁREZ-PINILLA P., GOÑI-CERVERA J., et al. Comparison of Mathematics Problem-Solving Abilities in Autistic and Non-autistic Children: the Influence of Cognitive Profile. Journal of Autism and Developmental Disorders, 2024, 54(1): 353–365, https://doi.org/10.1007/s10803-022-05802-w.

QOHAR A., and FAZIRA S. K. Student Mathematical Communication in Online Discussion in Introduction to Geometry Course using Edmodo. Journal of Education Research and Evaluation, 2022, 6(4): 576–585, https://doi.org/10.23887/jere.v6i4.51241.

YULIANA R. M., and HARTINI Students’ Thinking Process in Solving Mathematics Problems Reviewing from Cognitive Style. MaPan: Jurnal Matematika dan Pembelajaran, 2022, 10(2): 395–412, https://doi.org/10.24252/mapan.2022v10n2a10.

SON A. L., DARHIM, and FATIMAH S. Students’ Mathematical Problem-Solving Ability Based on Teaching Models Intervention and Cognitive Style. Journal on Mathematics Education, 2020, 11(2): 209–222.

AZMI S., BAIDOWI B., HIKMAH N., et al. Analysis of students’ mathematics communication ability based on cognitive styles and mathematical knowledge. Jurnal Pijar Mipa, 2022, 17(2): 231–238, https://doi.org/10.29303/jpm.v17i2.3384.

RUM A. M., and JUANDI D. Students Mathematical Literacy Viewed from Cognitive Style: Systematic Literature Review. Jambura Journal of Mathematics Education, 2023, 4(1): 1–10, https://doi.org/10.34312/jmathedu.v4i1.17438.

STROHMAIER A. R., REINHOLD F., HOFER S., et al. Different complex word problems require different combinations of cognitive skills. Educational Studies in Mathematics, 2022, 109(1): 89–114, https://doi.org/10.1007/s10649-021-10079-4.

COHEN L., MANION L., and MORRISON K. Research Methods in Education. 2017, https://doi.org/10.4324/9781315456539.

CRESWELL J. W., and CRESWELL J. D. Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. SAGE Publications International Educational and Professional Publisher, 2017.

YOO W. S., and PARK C. Y. Online group embedded figures test. Proceedings of the 7th International Conference on Information Technology Based Higher Education and Training, ITHET): 267–271, 2006, https://doi.org/10.1109/ITHET.2006.339774.

VERAWATI N. N. S. P., HIKMAWATI, PRAYOGI S., and BILAD M. R. Reflective Practices in Inquiry Learning: Its Effectiveness in Training Pre-Service Teachers’ Critical Thinking Viewed from Cognitive Styles. Jurnal Pendidikan IPA Indonesia, 2021, 10(4): 505–514, https://doi.org/10.15294/jpii.v10i4.31814.

ANDHESKA H., SUPARNO S., DAWUD D., and SUYITNO I. Writing motivation and the ability in writing a research proposal of generation Z students based on cognitive style. Journal for the Education of Gifted Young Scientists, 2020, 8(1): 87–104, https://doi.org/10.17478/jegys.651436.

SUTAMA S., et al. Metacognition of Junior High School Students in Mathematics Problem Solving Based on Cognitive Style. Asian Journal of University Education, 2021, 17(1): 134–144, https://doi.org/10.24191/ajue.v17i1.12604.

LAILIYAH S., MUSLIMAH N., and SUTINI, S. Do students with different cognitive styles have similar levels of statistical thinking? Beta: Jurnal Tadris Matematika, 2021, 14(1): 15–33, https://doi.org/10.20414/betajtm.v14i1.438.

ZHANG M., WANG X., WANG F., and LIU H. Effect of Cognitive Style on Language Control During Joint Language Switching: An ERP Study. Journal of Psycholinguistic Research, 2020, 49(3): 383–400, https://doi.org/10.1007/s10936-019-09682-7.

MILES M. B., HUBERMAN A. M., and SALDAÑA J. Qualitative data analysis, 2018, https://doi.org/10.1016/B978-0-08-102220-7.00019-4.

RAHMAWATI A., CHOLILY Y. M., and ZUKHRUFURROHMAH Z. Analyzing Students’ Mathematical Communication Ability in Solving Numerical Literacy Problems. Mosharafa: Jurnal Pendidikan Matematika, 2023, 12(1): 59–70, https://doi.org/10.31980/mosharafa.v12i1.1938.

AMNI, R. Analysis of Students’ Mathematical Communication Ability on Set Materials Based on Gender Differences. Journal of Research on Mathematics Instruction, 2021, 3(1): 1–13, https://doi.org/10.33578/jrmi.v3i1.56.

MASTUTI A. G., KALIKY S., and ARMAN J. Mathematical Communication and Students’ Epistemological Beliefs of Linear Systems with Three Variables. Jurnal Teori dan Aplikasi Matematika, 2022, 6(4): 963, https://doi.org/10.31764/jtam.v6i4.9772.

POLYA G. How to Solve it. Second Edition. New Jersey: Princeton University, 1973.

BATUBARA A. A. Dependent and Independent Cognitive Style Learning Model in Mathematics Subject Outcomes. Randwick International of Education and Linguistics Science Journal, 2023, 4(2): 323–331, https://doi.org/10.47175/rielsj.v4i2.701.

KALDARAS L. and WIEMAN C. Cognitive framework for blended mathematical sensemaking in science. International Journal of STEM Education, 2023, 10(1): 18, https://doi.org/10.1186/s40594-023-00409-8.

HÖFFLER T. N., KOĆ-JANUCHTA M., and LEUTNER D. More Evidence for Three Types of Cognitive Style: Validating the Object-Spatial Imagery and Verbal Questionnaire Using Eye Tracking when Learning with Texts and Pictures. Applied Cognitive Psychology, 2017, 31(1): 109–115, https://doi.org/10.1002/acp.3300.

HEIDARI K. A Psycholinguistic Look at the Role of Field Dependence/Independence in Receptive/Productive Vocabulary Knowledge: Does it Draw a Line? Journal of Psycholinguistic Research, 2022, 51(6): 1393–1408, https://doi.org/10.1007/s10936-022-09905-4.

ATABEK-YIGIT E. Can cognitive structure outcomes reveal cognitive styles? A study on the relationship between cognitive styles and cognitive structure outcomes on the subject of chemical kinetics. Chemistry Education Research and Practice, 2018, 19(3): 746–754, https://doi.org/10.1039/c8rp00018b.

SUNDAYANA R. and PARANI C. E. Analyzing Students’ Errors in Solving Trigonometric Problems Using Newman’s Procedure Based on Students’ Cognitive Style. Mosharafa: Jurnal Pendidikan Matematika, 2023, 12(1): 135–144, https://doi.org/10.31980/mosharafa.v12i1.2486.

GUISANDE M. A., PÁRAMO M. F., TINAJERO C., and ALMEIDA L. S. Field dependence-independence (FDI) cognitive style: An analysis of attentional functioning. Psicothema, 2007, 19(4): 572–577.

GIANCOLA M., PALMIERO M., and D’AMICO S. Field Dependent–Independent Cognitive Style and Creativity from the Process and Product-Oriented Approaches: a Systematic Review. Creativity Studies, 2022, 5(2): 542–559, https://doi.org/10.3846/cs.2022.15988.

UEGATANI Y. and OTANI H. A new ontology of reasons for inferentialism: redefining the notion of conceptualization and proposing an observer effect on assessment. Mathematics Education Research Journal, 2021, 33(1): 183–199, https://doi.org/10.1007/s13394-019-00289-8.

BRONKHORST H., ROORDA G., SUHRE C., and GOEDHART M. Logical Reasoning in Formal and Everyday Reasoning Tasks. International Journal of Science and Mathematics Education, 2020, 18(8): 1673–1694, https://doi.org/10.1007/s10763-019-10039-8.

ALEXANDER P. A. Individual differences in college-age learners: The importance of relational reasoning for learning and assessment in higher education. British Journal of Educational Psychology, 2019, 89(3): 416–428, https://doi.org/10.1111/bjep.12264.

HASBULLAH H., and SAJIMAN S. U. The Differences of Cognitive Style Fields-Independent and Dependent on Students’ Mathematical Problem Solving Abilities. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 2020, 9(2): 387–394, https://doi.org/10.24127/ajpm.v9i2.2778.

GIANCOLA M., D’AMICO S., and PALMIERO M. Working Memory and Divergent Thinking: The Moderating Role of Field-Dependent-Independent Cognitive Style in Adolescence. Behavioral Sciences, 2023, 13(5): 397, https://doi.org/10.3390/bs13050397.

CSÍKOS C. Metacognitive and Non-Metacognitive Processes in Arithmetic Performance: Can There Be More than One Meta-Level? Journal of Intelligence, 2022, 10(3): 53, https://doi.org/10.3390/jintelligence10030053.

WANG Y. and ZHENG L. A Novel Deep Framework for English Communication Based on Educational Psychology Perspective. Frontiers in Public Health, 2022, 10(June): 1–10, https://doi.org/10.3389/fpubh.2022.916101.

AGGARWAL I., SCHILPZAND M. C., MARTINS L. L., et al. The Benefits of Cognitive Style Versatility for Collaborative Work. Journal of Applied Psychology, 2022, 108(4): 647–659, https://doi.org/10.1037/apl0001035.

HILDRETH L. A., MILEY M., STRICKLAND E., and SWISHER J. Writing Workshops to Foster Written Communication Skills in Statistics Graduate Students. Journal of Statistics and Data Science Education, 2023, 31(2): 201–210, https://doi.org/10.1080/26939169.2022.2138800.

BIERER B. E., and BAEDORF KASSIS S. Communicating complex numeric information in clinical research. Frontiers in Communication, 2023, 8, https://doi.org/10.3389/fcomm.2023.1096271.


Refbacks

  • There are currently no refbacks.